To surf, jump or walk on to one of the curved walls (hereby referted to as 'ramps'). Then simply hold strafe (Default are the A and D keys). This will cause you to glide along the walls, or "surf".

While surfing, never press up, down, or crouch; pressing those will cause you to slide off the wall and fall, which, in most surf maps, will cause you to get sent back to your spawn.

To change direction (in order to make it to the next ramp), press the button for the direction you wish to go before flying off of your current ramp.

Maps with water surfaces, allow you to skee across them, while holding duck+jump key together.

Surfing takes practice, so don't be discouraged if you don't get it right the first time.